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A shoreline fumigation model with wind shear
Pergamoln
Atmosphmic Entinmment Vol. 29, No. 22 pp. 3373-3380.1995 Copyright 0 1995 Elswicr Scima Ltd Printed in Great Britain. All ri&ts -cd 1352-2310/95 $9.50 + 0.00
1352-2310(94)0023&7
A SHOR:ELINE FUMIGATION
MODEL WITH WIND SHEAR
LI ZHIBIAN and YAO ZENGQUAN Research Institute of Environmental Protection for Electric Power, 10 Pudong Road, Nanjing, 210031, People’s Republic of China (First received 1 January 1992 and in final form 31 July 1994)
Abstract-A fumigation model has been developed for a plume discharged from an elevated stack in a shoreline environment by introducing different wind directions above and within thermal internal boundary 1aye:r(TIBL) into a dispersion model. When a continuous point source. release occurs above the TIBL pollutants will disperse in the marine stable flow, until the plume intersects the TIBL surface. The fumigation in lthe TIBL is intefpreted as occurring from an area source on the imaginary surface of the TIBL. It is assumed that the wind direction varies with height above and below L(x) = AX’, the heighhtof the TIBL at the distance x. The change of wind direction above and within the TIBL causes the pollutants to change their direction of transport and leads to development of a curved ground level concentration (glc) axis; a decreasmg glc along the centreline of the fumigation and a widening pollutant distribution in the transverse direction. Predicted concentration distributions using the wind shear model are compared with observations from an SF, tracer experiment near Hangzhou Bay in May-June of 1987. The comparison and an evaluation of the model performance show that the new model is not only more theoretically acceptable than those based on empirical coefficients but also provides concentration distributions which agree well with SF6 tracer experiments. Key word index: Coast, fumigation, dispersion model, wind shear.
1. INTRODUCTION
In
the coastal area, when maritime stable air flows over land heated by solar radiation in on-shore winds, a thermal internal boundary layer (TIBL) frequently develops over the land. Pollutants emitted from an elevated source locat.ed near the shoreline will intersect the TIBL which increases in depth with distance from the shoreline, and will be brought to the surface as a result of the strong mixing action in the TIBL resulting in a ground level fumigation and potentially high concentrations of a pollutant. The fumigation may persist for hours. Figure 1 shows an example of the coast fumigation situations observed near Hang Zoug Bay using plume image analysis system at 11: 00- 11: 20 on June 3 of 1987. The figure is an average photograph overlapped from 30 images taken in 20 min. Every colour on the picture represents one certain concentration scope. This coal fuel fired power station is located about 4 km from shoreline and the chimney height is 210 m. When SF6 gas was released from the chimney in the period, high concentrations of SF6 were monitored at ground level in the downwind area also. Lyons and Cole (1973), van Dop et al. (1979) and Misra (1980) developed fumigation models based on atmospheric dispersion theory and results of field experiments. Deardorff and Willis (1982) and Stunder
and SethuRaman (1986) modified the assumption of instantaneous mixing in the vertical direction in earlier models to represent atmospheric p?ocesses more realistically. All of the models assume a constant wind direction above and within the TIBL. Results of on-site experiments conducted between 1986 and 1988 in eastern Chinese coastal areas show that the wind direction and velocity in the upper stable layer is significantly different from that within the TIBL. Among 143 cases with an observed TIBL, 36% of the samples have a value of CY (the difference between the average wind direction D2 in the TIBL and D1 up to 400m above the TIBL) less than 15”; 35% have a value of a between 15” and 45”, and in 29% of the cases a is greater than 45”. In SF, tracer experiments near Hangzhou Bay in May-June 1987 it was observed that the centre line of the ground level concentration (glc) in the fumigation increasingly deflects with increasing downwind distance and the glc concentration distribution is more homogeneous than that predicted by the Misra (1980) model. Wind shear simultaneous with an abrupt transition of temperature with height (Fig. 2) is an important characteristic of the atmospheric boundary layer when a TIBL exists and their impact on dispersion patterns is significant. A factor F (U sin a/W., where W. is convective sealing velocity) was introduced by Deardorff and Willis
3373
LI ZHIBIAN and YAO ZENGQUAN
Fig. 1. Fumigation phenomenon of elevated plume near coast (observed at Zenghai Power Plant near Hang Zhou Bay, 3 June 1987, 11 :Ot-11 : 20).
500 400
g
300
X 200
100 0
1234
0
WS (m/s)
90 WD (“)
180
0
294
296
298
PT (“K)
Fig. 2 Profiles of wind direction (WD), wind speed (WS) and potential temperature (PT). (30 May, 11: 00, solid line and 11 June, 10: 40,dotted line.)
(1982) to predict more closely the centreline glc when the wind shear exists (Cm(x,O) = FC(x,O)). This modification reduces the glc on the centreline of the plume greatly. Pasquill and Smith (1983) introduced a factor dependent on wind shear angle to enlarge the transverse dispersion coefficient as follows: 2 = c,’ + 0.03 a2x2; where by is the horizontal disOYC persion coefficient without considering the effect of the wind shear, uyc includes the effect of the wind shear and x is downwind distance from the source. With this modification, the predicted maximum ground level concentration is also greatly reduced. In this paper a new shoreline fumigation model in which the atmospheric boundary layer is divided into
two layers (a layer above the TIBL and the layer within the TIBL) is developed. Different wind directions and velocities in the two layers are used to calculate the concentration. Meteorological observations and SF6 tracer experiments near Hangzhou Bay in May-June of 1987 were used to evaluate performance of the 2-layer model.
2. TRACER EXPERIMENTS SF6 tracer was released 500 m inland from the shoreline at about 200m height which was above the TIBL at this location. A 6 mm diameter polyvinyl tube was carried up to
Shoreline fumigation model 200 m level using a 10 mJ balloon. The exact release height was measured using a theodolite and laser range finder. The tube was connected to an SF6 tank at the ground equipped with a pressure regulat,or valve and flowmeter. The tank was equipped with an electric heater to keep the temperature of gasified SF6 tracer at or slightly above the ambient temperature. The emission rate was regulated using the flowmeter and the total release mass was determined by weighing the tank before and after a release. Receptors were locat.ed at 10”intervals out to 60” on both sides of a line normal to the coast along arcs at 610, 3400, 5000, 7000 and 9000 m from the release point. On the line normal to the coast at 610,340O and So00 m samplers were located 50, 100, 150, 200 and 250 m above the ground. The period of release was determined using real-time wind measurements. Sampling was conducted for 30 or 60min during releases which lasted 45 or 90 min. Three or six samples of 10 min duration were collected depending on persistence of the wind direction. Samplers were controlled remotely with the sample timing determined using measured wind velocities. A meteorological observation program was conducted simultaneously with the SF6 sampling program. Temperature, wind speed, wind direction and turbulence above the sea surface were measured at two levels (1.5 and 14 m). Wind velocity and temperature profiles from 2 to 500 m were observed at the release site using a tethersonde system.
3. MODEL DEVELOPMENT When a continuous point source release occurs above the TIBL pollutants will disperse in the marine stable flow until the plume intersects the TIBL surface. The fumigation in the TIBL is interpreted as occurring from an area source on the imaginary surface of the TIBL. It i:s assumed that the wind direction varies with height above and below L(x) = Ax*, the height of the TIBL at the distance x. Using a 2-layer model as a first approximation, above the TIBL the mean wind direction and speed are taken to be D, and Ut, respectively Within the TIBL, the mead wind direction and speed are D2 and iJ2 (Fig. 3). In a polar co-ordinates (R, 0, Z), 0 is zero to the north.
3375
Intheregion(-cc
(1) x1
=
-
RI cos(0,
- Dl)
(24
y, = RI sin@, - Oi)
(2b)
where cF(xi) and u,(xi) are the cross-wind and vertical standard deviations of concentration at downwind distance xi from the source. H, a,(xJ and c&x1) are functions of upper wind speed Ui. Transport of pollutants from this region into the TIBL occurs by two mechanisms: 1. Entrainment of the pollutants due to the downwind increase of the TIBL height L(x). 2. Diffusion of the pollutants into the TIBL by processes which disperse the plume in the stable layer. This results in a net flux F(x, y) of the pollutants through the top surface of the TIBL: F(x, Y) = Cs(x,
YP Jw)
K,,aC,
dL Ul
z
+
(3)
-y-j-
s z
>
where K,, is vertical dispersion coefficient in stable layer and is a function of Q,,: K,
P(R,e)
=ff$
I
S
Fig. 3. Illustration of definition of x2, y,.
3316
LI ZHIBIAN and YAO ZENGQUAN
Substituting
K,, and C, in equation (3)
F(x,y)=
UIC,
dL
and within the TIBL are the same, the tquation reduces to the Misra (1980) coastline fumigation model.
L-H&,,
(5)
This implies that at each point (R,, 0,) on the upper surface of the TIBL, there is a source of strength dq(R1, 0,) = F(x,, Y,, L(x,))R, dRi dBr. The source emits into the TIBL (- cc < y < + q0 6 z < L(x) and 0 < x < + co) at wind speed V2, along the wind direction Dz. Assuming a Gaussian cross-wind distribution of the pollutants and a uniform vertical distribution within the TIBL the concentration due to dq(R,, I!?,)at point (R, 0) within TIBL is given by dC(R, 6) =
exp (-S&J)
Jinvz;(x,)L(x)
(6)
where, x = - R cos(8 - Dl), oYU(xz)is the cross-wind standard deviation of concentration at distance x2, (R,, 0,) is taken as origin in calculating x2 and y,. Referring to Fig. 3 if the origin of dq is at 0 1(R i, 0,) and P(R, 0) is a receptor point, then the length of the path from 0, to P is OIP=
R’+R:-2RR,cos(8-8,)
cp = arccos
(7)
01P2 + R: - R2
(8)
2R101P
x2 = 0,Pcosa
(94
y, = 0,Psinor
(W
CI= (0, - D,) - q
e > e1
(le - e,l G 180”)
.cI= 2x -
(e, - D2) - cp
e < e,(le
- e,l G 180”).
(104
(lob)
The ground level concentration distribution of pollutant from the area source on the TIBL surface can be obtained by integrating equation (6)
-Xx,) - H(x,) do&r) xRidR,dB,.
1 (11)
Equation (11) describes the concentration distribution in 3-dimensional space, using polar co-ordinates, for a fumigation within a TIBL when wind shear occurs across the TIBL surface; i.e. for the wind shear fumigation model. When the effective stack height does not vary with the distance and the wind above
4. EVALUATION
OF THE MODEL
Data from observations described above for 30 May and 11 June 1987 were used to evaluate the model. On 30 May and 11 June 1987 large scale meteorological conditions were dominated by anticyclonic weak gradient wind and on-shore flow persisted during the days. The coastal TIBL began to form about 09:OO and persisted until about 17: 00. Figure 2 presents the profiles of wind direction, wind speed and potential temperature with height above the tracer release site at 11: 00 and 10 : 40 on 30 May and 11 June 1987. In Fig. 2, the dashed line indicates the TIBL heights at the time noted. The change of wind speed, wind direction and temperature from the layer above the TIBL to the surface is significant on both the days. 4.1. Comparison of prediction and observation The change of wind direction above and within the TIBL causes the pollutants change their direction of transport and leads to development of a curved glc axis; a decreasing glc along the centreline of the fumigation and a widening pollutant distribution in the transverse direction. These features are observed in the SF, field experiment and are predicted accurately using the wind shear model. Comparisons are discussed below. (a) The dejection of ground concentration axis with increasing distance. The predicted glc values using a model with no wind shear (Misra, 1980), called MSFM, and with the wind shear model described in this paper, called WSFM, for meteorological conditions observed on 11 June are presented in Fig. 4a and b respectively. The observed SF6 glc distribution for 11 June 1987 is given in Fig. 4c. The dashed line in the figures is the average centreline of the glc in the one hour and the lattered circle is the location of maximum ground concentration along the arcs at the surface for observation cases A-F during 10:40-11: 40. It is clear that with an increase of distance from the source, the axis of the maximum ground concentrations calculated using the wind shear model deviates gradually from wind direction D, in the upper layer toward the D2 in the lower layer, Fig. 4b, in an agreement with the observed deflection of average concentration axis in the hour as shown by the dashed curve in Fig. 4c. (b) The decrease of maximum ground concentration. Taking into account the effect of wind direction shear, the WSFM and the models of Deardorff and Willis (1982) and Stunder and SethuRaman (1986) give a maximum ground concentration (C,,,) lower than that when the flow field is uniform in the vertical. The predicted values of maximum ground concentration with different shear angles GLof wind direction
Shoreline fumigation model
(c) Observed
5km
\
Fig. 4. (a) The concentration distribution predicted by MSFM. (b) The concentration distribution predicted by WSFM. (c) The centre line of the monitored SF6 glc.
under the condition of June 11 for the wind shear model (WSFM), the Misra model using an increased
dispersion parameter u& = uf + 0.03 a*~* (Pasquill and Smith, 1983) (PSFM) and modified centreline glc
3311
with a factor F = U sin a/ W., Cm(x, 0) = FCo(x, 0) (Deardorff and Willis, 1983) (DSFM) are shown in Table 1. When a = O”, the values of C,,, in Table 1 correspond to those predicted by the Misra model (MSFM). The observed value in Table 1 is the maximum mean ground concentration of SF6 during 10:40-11:40. The decrease in predicted concentration using the WSFM model presented here is more gradual than that predicted by the other models reviewed and is in good agreement with the observed value for a wind direction shear of 34” observed on 11 June 1987 in a clearly defined fumigation case. (c) The widening of the horizontal distribution of ground concentration. The scope of the pollutant horizontal dispersion is primarily determined by the horizontal dispersion coefficient Q,,used in the model. The coefficients used in the predictions presented here were calculated using the turbulence measurements of wind and temperature in addition to neutrally buoyant pilot balloon data observed during several experiments in the Hangzhou Bay region (Yao and Li, 1992). In a field experiment at a Lake Michigan site, Lyons and Cole (1973) observed that the stability classification based on a, was usually E or D and never F, while that based on u,, was usually F. On the basis of their findings, for the stable layer above the TIBL, we used a value of a, corresponding to stability class E and a 6, corresponding to stability class F and 0,. as stability class A-B for the layer within TIBL in the predictions of the models. Table 2 compares the o;(x) calculated using the models described in this paper with that evaluated using the observed distribution of SF6 at ll:OC-16:00 on 30 May and at lO:OO-14:00 on 11 June 1987. Table 2 shows the standard deviation of horizontal concentration distribution, a;, calculated using the observed ground SF6 concentration and the & calculated using the ground concentration distribution predicted using the models. The a;, and &, are averages based on dispersion through both stable and unstable layers. The uLP values calculated using the WSFM are in good agreement with those calculated using observed concentration distributions and are larger than those predicted using MSFM and PSFM. From the ground concentration distribution given by the Fig. 4, we can also see that taking into account the effect of wind direction shear, the width of the horizontal ground
Table 1. The maximum ground concentration Cm as a function of wind shear angle a (degree) Model WSFM PSFM DSFM Observed
0
5
11
22.5
34
45
61.5
90
11.56 11.56 11.56
11.42 11.26 10.20
10.09 10.25 7.13
8.92 8.06 4.76
7.56 6.35 3.24 8.48
6.40 5.15 2.31
5.36 3.66 2.03
4.02 2.82 1.85
LI ZHIBIAN and r’A0 ZENGQUAN
3378
Table 2. The standard deviation of horizontal ground concentration distribution predicted using various models Downwind distance Date
Model
3.4 (km)
5.5 (km)
30 May
MSFM PSFM WSFM Observed
c& u;, c;, u;,,
222 m 332 m 386 m 443m
417 m 452 m 561 m 553 m
11 June
MSFM PSFM WSFM Observed
c& %P *;p ok0
223 m 332 m 402 m 408 m
417m 452 m 596 m 568 m
4.2. Statistical evaluation of the models
Using the statistical analysis procedures described by Willmott (1982) a more rigorous and objective comparison of model predictions and observed concentrations can be made. The statistical analysis includes calculation of c,,, the mean value of observed ground concentrations Coi, and c,, the mean of predicted values C,i, and their standard deviations S, and S, defined as follows:
(12) The closer cP is to C,, and the less the difference between S, and S,, the closer the predicted concentra-
distribution is greater. At larger wind shear angles, existing fumigation models do not predict that such large area will be seriously polluted. (d) Comparison of ground concentration. Figure 5 compares the predicted SF, concentrations using WSFM for c( = 0” and for observed 01with the observed concentrations for the two day conditions when a TIBL and a wind direction shear existed. The dashed lines correspond to a factor of two greater and less than the observed value. The percentage of predicted values falling within the region is about 80% for the case where c(equals observed values but about 55% if wind shear direction is not included for the calculation (GI= 00). The figures indicate better agreement at high concentrations. Figure 6 shows a comparison of predicted and observed concentrations for a very large coal fired generating station at Nanticoke Complex in Ontario, Canada. Data are from Misra and Onlock (1982) and Hoff et al. (1982). More than 90% of the observed values are within a factor of two of the values predicted using the mode1 proposed here.
(a)
IO0
MSFM
IO’
Observed (pg mS3)
10
10
1000
100
10,000
Observed (pg me3)
Fig. 6. The comparison between the values predicted by WFSM and the observed at Nanticoke Complex.
(b) WSFM
IO0
IO'
Observed (pg mm3)
Fig. 5. (a) Comparison between the values predicted by MFSM and the observed. (b) Comparison between the values predicted by WFSM and the observed.
Shoreline fumigation model
3379
Table 3. WSFM evaluating results for a = 0’ and for observed a
Model
C,
MSFM a = 0” WSFM Observed
C,
S,,
2.49 4.75
4.02 5.96
6.33
d
S,
- 3.84 63.07 - 1.75 31.24
(13)
,$(C,i - Co)’
(14)
(Cri - Cr)’.
(15)
I-1
Si = f ,i 1-l
The difference assessment includes estimation of the bias d; the difference between prediction and observation; the variance of the difference S’; the mean absolute gross error IdI and the mean square error MSE with its systematic component MSEs and its unsystematic component MSE,. They are defined respectively as follows:
d= jj ,i
Idl
MSE
MSE,
MSE.
h
5.58 3.47
76.38 33.61
65.96 23.42
10.43 10.19
0.59 0.85
9.55
tion to the observed one;
St = f
S2
(Cpi
-
where Cbi = Cri - C,,, Cbi = C,i - C,,. The agreement index h falls between 0 and 1. As the index approaches 1, performance of the model improves. Table 3 shows the results of evaluating the proposed model for CI= 0” and for observed CIusing these parameters. The agreement between C, and Cr, and between S, and S, is better for observed c( in the model. All of the difference evaluation parameters for observed tl are smaller than for a = 0”. Willmott’s agreement index h is 0.59 for t( = 0” and increases to 0.85 for observed a. Clearly the concentration distribution predicted by the WSFM when the direction shear is included is in better agreement with the observed values.
5. CONCLUSIONS
Coil
I-l
S* =’
jj
[(Cpi
,i
C&) - J]*
-
(17)
I-1
IdI =
Y$ ,i ICpi-
Coil
(18)
t-l
MSE = f ,i
(Cri - C,J*
(19)
1-l
MSE, = $ ,i
(c^p- C,i)*
t-l
MSE, =. ;
,;
(Cpi - c^,)’
(21)
1-l
where (3, = arCo + br and a1 and bl are the slope and the intercept of the regression line. The smaller the value of these variables, the more accurate will be the model. The larger systematic component of mean square error (MSE,) shows that the model has not yet been able to describe physical phenomena in all respects and should be further refined. The index of agreement h, is expressed as the following:
h=l-
E
;=1
fcoi - Cpi)*
iC, (Icbil + Icbil)*
(22)
The ground concentration distribution predicted by the shoreline fumigation model with wind shear (WSFM) has the following characteristics: (1) The centre line of the ground concentration deflects from the mean wind direction above the TIBL Dr to that within the TIBL D2 with increasing distance. (2) The maximum ground concentration decreases slowly with increased wind direction shear angle. (3) The width of the ground concentration horizontal distribution is greater. Increasing the area predicted to be affected by a fumigation due to an elevated plume intersecting a TIBL in a coastal region. Predicted concentration distributions are compared with observations from an SF6 tracer experiment when wind shear occurred in a coastal region. The wind shear fumigation model developed in this paper provides predictions in better agreement with observations when wind direction shear is included.
REFERENCES
Deardorff J. C. and Willis G. E. (1982) Ground-level concentrations due to fumigation into an entraining mixed layer. Atmospheric Environment 16, 1159-1170. HoflR. M., Trivett N. B. A., Millan M. M., Fellin P., Anlauf K. G., Wiebe H. A. and Bell R. (1982) The Nanticoke shoreline diffusion experiment, June 1978-111. Groundbased air quality measurements. Atmospheric Enoironment 16.439-454.
3380
LI ZHIBIAN and YAO ZENGQUAN
Lyons W. A. and Cole H. S. (1973) Fumigation and plume trapping on the shores of lake Michigan during stable onshore flows. J. appl. Met. 12, 4955’10. Misra P. K. (1980) Dispersion from tall stacks into a shoreline environment. Atmospheric Environment 14, 397-400. Misra P. K. and Onlock S. (1982) Modelling continuous fumigation of Nanticoke Generating Station plume. Atmospheric Environment 16, 479-489.
Pas&ill F. A. and Smith F. B. (1983) Atmospheric Difision, 3rd Edn. Wiley, New York, p. 437. Stunder M. and SethuRaman S. (1986) Downwind non-
uniform
mixing
in shoreline
fumigation
processes.
Boundary-Layer Met. 34, 177-184.
Van Dop H., Steenkist R. and Nieuwstadt F. T. M. (1979) Revised estimates for continuous shoreline fumigation. J. appl. Met. 18, 133-137. Willmott C. J. (1982) Some comments on the evaluation of model performance. Bull. Am. met. Sot. 63, 1309-1313. Yao Z. Q. and Li Z. B. (1992) The characteristics of turbulence and dispersion in surface layer of coastal region. J. Hydrodyn. Ser. B 3, 67-78.
Atmosphmic Entinmment Vol. 29, No. 22 pp. 3373-3380.1995 Copyright 0 1995 Elswicr Scima Ltd Printed in Great Britain. All ri&ts -cd 1352-2310/95 $9.50 + 0.00
1352-2310(94)0023&7
A SHOR:ELINE FUMIGATION
MODEL WITH WIND SHEAR
LI ZHIBIAN and YAO ZENGQUAN Research Institute of Environmental Protection for Electric Power, 10 Pudong Road, Nanjing, 210031, People’s Republic of China (First received 1 January 1992 and in final form 31 July 1994)
Abstract-A fumigation model has been developed for a plume discharged from an elevated stack in a shoreline environment by introducing different wind directions above and within thermal internal boundary 1aye:r(TIBL) into a dispersion model. When a continuous point source. release occurs above the TIBL pollutants will disperse in the marine stable flow, until the plume intersects the TIBL surface. The fumigation in lthe TIBL is intefpreted as occurring from an area source on the imaginary surface of the TIBL. It is assumed that the wind direction varies with height above and below L(x) = AX’, the heighhtof the TIBL at the distance x. The change of wind direction above and within the TIBL causes the pollutants to change their direction of transport and leads to development of a curved ground level concentration (glc) axis; a decreasmg glc along the centreline of the fumigation and a widening pollutant distribution in the transverse direction. Predicted concentration distributions using the wind shear model are compared with observations from an SF, tracer experiment near Hangzhou Bay in May-June of 1987. The comparison and an evaluation of the model performance show that the new model is not only more theoretically acceptable than those based on empirical coefficients but also provides concentration distributions which agree well with SF6 tracer experiments. Key word index: Coast, fumigation, dispersion model, wind shear.
1. INTRODUCTION
In
the coastal area, when maritime stable air flows over land heated by solar radiation in on-shore winds, a thermal internal boundary layer (TIBL) frequently develops over the land. Pollutants emitted from an elevated source locat.ed near the shoreline will intersect the TIBL which increases in depth with distance from the shoreline, and will be brought to the surface as a result of the strong mixing action in the TIBL resulting in a ground level fumigation and potentially high concentrations of a pollutant. The fumigation may persist for hours. Figure 1 shows an example of the coast fumigation situations observed near Hang Zoug Bay using plume image analysis system at 11: 00- 11: 20 on June 3 of 1987. The figure is an average photograph overlapped from 30 images taken in 20 min. Every colour on the picture represents one certain concentration scope. This coal fuel fired power station is located about 4 km from shoreline and the chimney height is 210 m. When SF6 gas was released from the chimney in the period, high concentrations of SF6 were monitored at ground level in the downwind area also. Lyons and Cole (1973), van Dop et al. (1979) and Misra (1980) developed fumigation models based on atmospheric dispersion theory and results of field experiments. Deardorff and Willis (1982) and Stunder
and SethuRaman (1986) modified the assumption of instantaneous mixing in the vertical direction in earlier models to represent atmospheric p?ocesses more realistically. All of the models assume a constant wind direction above and within the TIBL. Results of on-site experiments conducted between 1986 and 1988 in eastern Chinese coastal areas show that the wind direction and velocity in the upper stable layer is significantly different from that within the TIBL. Among 143 cases with an observed TIBL, 36% of the samples have a value of CY (the difference between the average wind direction D2 in the TIBL and D1 up to 400m above the TIBL) less than 15”; 35% have a value of a between 15” and 45”, and in 29% of the cases a is greater than 45”. In SF, tracer experiments near Hangzhou Bay in May-June 1987 it was observed that the centre line of the ground level concentration (glc) in the fumigation increasingly deflects with increasing downwind distance and the glc concentration distribution is more homogeneous than that predicted by the Misra (1980) model. Wind shear simultaneous with an abrupt transition of temperature with height (Fig. 2) is an important characteristic of the atmospheric boundary layer when a TIBL exists and their impact on dispersion patterns is significant. A factor F (U sin a/W., where W. is convective sealing velocity) was introduced by Deardorff and Willis
3373
LI ZHIBIAN and YAO ZENGQUAN
Fig. 1. Fumigation phenomenon of elevated plume near coast (observed at Zenghai Power Plant near Hang Zhou Bay, 3 June 1987, 11 :Ot-11 : 20).
500 400
g
300
X 200
100 0
1234
0
WS (m/s)
90 WD (“)
180
0
294
296
298
PT (“K)
Fig. 2 Profiles of wind direction (WD), wind speed (WS) and potential temperature (PT). (30 May, 11: 00, solid line and 11 June, 10: 40,dotted line.)
(1982) to predict more closely the centreline glc when the wind shear exists (Cm(x,O) = FC(x,O)). This modification reduces the glc on the centreline of the plume greatly. Pasquill and Smith (1983) introduced a factor dependent on wind shear angle to enlarge the transverse dispersion coefficient as follows: 2 = c,’ + 0.03 a2x2; where by is the horizontal disOYC persion coefficient without considering the effect of the wind shear, uyc includes the effect of the wind shear and x is downwind distance from the source. With this modification, the predicted maximum ground level concentration is also greatly reduced. In this paper a new shoreline fumigation model in which the atmospheric boundary layer is divided into
two layers (a layer above the TIBL and the layer within the TIBL) is developed. Different wind directions and velocities in the two layers are used to calculate the concentration. Meteorological observations and SF6 tracer experiments near Hangzhou Bay in May-June of 1987 were used to evaluate performance of the 2-layer model.
2. TRACER EXPERIMENTS SF6 tracer was released 500 m inland from the shoreline at about 200m height which was above the TIBL at this location. A 6 mm diameter polyvinyl tube was carried up to
Shoreline fumigation model 200 m level using a 10 mJ balloon. The exact release height was measured using a theodolite and laser range finder. The tube was connected to an SF6 tank at the ground equipped with a pressure regulat,or valve and flowmeter. The tank was equipped with an electric heater to keep the temperature of gasified SF6 tracer at or slightly above the ambient temperature. The emission rate was regulated using the flowmeter and the total release mass was determined by weighing the tank before and after a release. Receptors were locat.ed at 10”intervals out to 60” on both sides of a line normal to the coast along arcs at 610, 3400, 5000, 7000 and 9000 m from the release point. On the line normal to the coast at 610,340O and So00 m samplers were located 50, 100, 150, 200 and 250 m above the ground. The period of release was determined using real-time wind measurements. Sampling was conducted for 30 or 60min during releases which lasted 45 or 90 min. Three or six samples of 10 min duration were collected depending on persistence of the wind direction. Samplers were controlled remotely with the sample timing determined using measured wind velocities. A meteorological observation program was conducted simultaneously with the SF6 sampling program. Temperature, wind speed, wind direction and turbulence above the sea surface were measured at two levels (1.5 and 14 m). Wind velocity and temperature profiles from 2 to 500 m were observed at the release site using a tethersonde system.
3. MODEL DEVELOPMENT When a continuous point source release occurs above the TIBL pollutants will disperse in the marine stable flow until the plume intersects the TIBL surface. The fumigation in the TIBL is interpreted as occurring from an area source on the imaginary surface of the TIBL. It i:s assumed that the wind direction varies with height above and below L(x) = Ax*, the height of the TIBL at the distance x. Using a 2-layer model as a first approximation, above the TIBL the mean wind direction and speed are taken to be D, and Ut, respectively Within the TIBL, the mead wind direction and speed are D2 and iJ2 (Fig. 3). In a polar co-ordinates (R, 0, Z), 0 is zero to the north.
3375
Intheregion(-cc
(1) x1
=
-
RI cos(0,
- Dl)
(24
y, = RI sin@, - Oi)
(2b)
where cF(xi) and u,(xi) are the cross-wind and vertical standard deviations of concentration at downwind distance xi from the source. H, a,(xJ and c&x1) are functions of upper wind speed Ui. Transport of pollutants from this region into the TIBL occurs by two mechanisms: 1. Entrainment of the pollutants due to the downwind increase of the TIBL height L(x). 2. Diffusion of the pollutants into the TIBL by processes which disperse the plume in the stable layer. This results in a net flux F(x, y) of the pollutants through the top surface of the TIBL: F(x, Y) = Cs(x,
YP Jw)
K,,aC,
dL Ul
z
+
(3)
-y-j-
s z
>
where K,, is vertical dispersion coefficient in stable layer and is a function of Q,,: K,
P(R,e)
=ff$
I
S
Fig. 3. Illustration of definition of x2, y,.
3316
LI ZHIBIAN and YAO ZENGQUAN
Substituting
K,, and C, in equation (3)
F(x,y)=
UIC,
dL
and within the TIBL are the same, the tquation reduces to the Misra (1980) coastline fumigation model.
L-H&,,
(5)
This implies that at each point (R,, 0,) on the upper surface of the TIBL, there is a source of strength dq(R1, 0,) = F(x,, Y,, L(x,))R, dRi dBr. The source emits into the TIBL (- cc < y < + q0 6 z < L(x) and 0 < x < + co) at wind speed V2, along the wind direction Dz. Assuming a Gaussian cross-wind distribution of the pollutants and a uniform vertical distribution within the TIBL the concentration due to dq(R,, I!?,)at point (R, 0) within TIBL is given by dC(R, 6) =
exp (-S&J)
Jinvz;(x,)L(x)
(6)
where, x = - R cos(8 - Dl), oYU(xz)is the cross-wind standard deviation of concentration at distance x2, (R,, 0,) is taken as origin in calculating x2 and y,. Referring to Fig. 3 if the origin of dq is at 0 1(R i, 0,) and P(R, 0) is a receptor point, then the length of the path from 0, to P is OIP=
R’+R:-2RR,cos(8-8,)
cp = arccos
(7)
01P2 + R: - R2
(8)
2R101P
x2 = 0,Pcosa
(94
y, = 0,Psinor
(W
CI= (0, - D,) - q
e > e1
(le - e,l G 180”)
.cI= 2x -
(e, - D2) - cp
e < e,(le
- e,l G 180”).
(104
(lob)
The ground level concentration distribution of pollutant from the area source on the TIBL surface can be obtained by integrating equation (6)
-Xx,) - H(x,) do&r) xRidR,dB,.
1 (11)
Equation (11) describes the concentration distribution in 3-dimensional space, using polar co-ordinates, for a fumigation within a TIBL when wind shear occurs across the TIBL surface; i.e. for the wind shear fumigation model. When the effective stack height does not vary with the distance and the wind above
4. EVALUATION
OF THE MODEL
Data from observations described above for 30 May and 11 June 1987 were used to evaluate the model. On 30 May and 11 June 1987 large scale meteorological conditions were dominated by anticyclonic weak gradient wind and on-shore flow persisted during the days. The coastal TIBL began to form about 09:OO and persisted until about 17: 00. Figure 2 presents the profiles of wind direction, wind speed and potential temperature with height above the tracer release site at 11: 00 and 10 : 40 on 30 May and 11 June 1987. In Fig. 2, the dashed line indicates the TIBL heights at the time noted. The change of wind speed, wind direction and temperature from the layer above the TIBL to the surface is significant on both the days. 4.1. Comparison of prediction and observation The change of wind direction above and within the TIBL causes the pollutants change their direction of transport and leads to development of a curved glc axis; a decreasing glc along the centreline of the fumigation and a widening pollutant distribution in the transverse direction. These features are observed in the SF, field experiment and are predicted accurately using the wind shear model. Comparisons are discussed below. (a) The dejection of ground concentration axis with increasing distance. The predicted glc values using a model with no wind shear (Misra, 1980), called MSFM, and with the wind shear model described in this paper, called WSFM, for meteorological conditions observed on 11 June are presented in Fig. 4a and b respectively. The observed SF6 glc distribution for 11 June 1987 is given in Fig. 4c. The dashed line in the figures is the average centreline of the glc in the one hour and the lattered circle is the location of maximum ground concentration along the arcs at the surface for observation cases A-F during 10:40-11: 40. It is clear that with an increase of distance from the source, the axis of the maximum ground concentrations calculated using the wind shear model deviates gradually from wind direction D, in the upper layer toward the D2 in the lower layer, Fig. 4b, in an agreement with the observed deflection of average concentration axis in the hour as shown by the dashed curve in Fig. 4c. (b) The decrease of maximum ground concentration. Taking into account the effect of wind direction shear, the WSFM and the models of Deardorff and Willis (1982) and Stunder and SethuRaman (1986) give a maximum ground concentration (C,,,) lower than that when the flow field is uniform in the vertical. The predicted values of maximum ground concentration with different shear angles GLof wind direction
Shoreline fumigation model
(c) Observed
5km
\
Fig. 4. (a) The concentration distribution predicted by MSFM. (b) The concentration distribution predicted by WSFM. (c) The centre line of the monitored SF6 glc.
under the condition of June 11 for the wind shear model (WSFM), the Misra model using an increased
dispersion parameter u& = uf + 0.03 a*~* (Pasquill and Smith, 1983) (PSFM) and modified centreline glc
3311
with a factor F = U sin a/ W., Cm(x, 0) = FCo(x, 0) (Deardorff and Willis, 1983) (DSFM) are shown in Table 1. When a = O”, the values of C,,, in Table 1 correspond to those predicted by the Misra model (MSFM). The observed value in Table 1 is the maximum mean ground concentration of SF6 during 10:40-11:40. The decrease in predicted concentration using the WSFM model presented here is more gradual than that predicted by the other models reviewed and is in good agreement with the observed value for a wind direction shear of 34” observed on 11 June 1987 in a clearly defined fumigation case. (c) The widening of the horizontal distribution of ground concentration. The scope of the pollutant horizontal dispersion is primarily determined by the horizontal dispersion coefficient Q,,used in the model. The coefficients used in the predictions presented here were calculated using the turbulence measurements of wind and temperature in addition to neutrally buoyant pilot balloon data observed during several experiments in the Hangzhou Bay region (Yao and Li, 1992). In a field experiment at a Lake Michigan site, Lyons and Cole (1973) observed that the stability classification based on a, was usually E or D and never F, while that based on u,, was usually F. On the basis of their findings, for the stable layer above the TIBL, we used a value of a, corresponding to stability class E and a 6, corresponding to stability class F and 0,. as stability class A-B for the layer within TIBL in the predictions of the models. Table 2 compares the o;(x) calculated using the models described in this paper with that evaluated using the observed distribution of SF6 at ll:OC-16:00 on 30 May and at lO:OO-14:00 on 11 June 1987. Table 2 shows the standard deviation of horizontal concentration distribution, a;, calculated using the observed ground SF6 concentration and the & calculated using the ground concentration distribution predicted using the models. The a;, and &, are averages based on dispersion through both stable and unstable layers. The uLP values calculated using the WSFM are in good agreement with those calculated using observed concentration distributions and are larger than those predicted using MSFM and PSFM. From the ground concentration distribution given by the Fig. 4, we can also see that taking into account the effect of wind direction shear, the width of the horizontal ground
Table 1. The maximum ground concentration Cm as a function of wind shear angle a (degree) Model WSFM PSFM DSFM Observed
0
5
11
22.5
34
45
61.5
90
11.56 11.56 11.56
11.42 11.26 10.20
10.09 10.25 7.13
8.92 8.06 4.76
7.56 6.35 3.24 8.48
6.40 5.15 2.31
5.36 3.66 2.03
4.02 2.82 1.85
LI ZHIBIAN and r’A0 ZENGQUAN
3378
Table 2. The standard deviation of horizontal ground concentration distribution predicted using various models Downwind distance Date
Model
3.4 (km)
5.5 (km)
30 May
MSFM PSFM WSFM Observed
c& u;, c;, u;,,
222 m 332 m 386 m 443m
417 m 452 m 561 m 553 m
11 June
MSFM PSFM WSFM Observed
c& %P *;p ok0
223 m 332 m 402 m 408 m
417m 452 m 596 m 568 m
4.2. Statistical evaluation of the models
Using the statistical analysis procedures described by Willmott (1982) a more rigorous and objective comparison of model predictions and observed concentrations can be made. The statistical analysis includes calculation of c,,, the mean value of observed ground concentrations Coi, and c,, the mean of predicted values C,i, and their standard deviations S, and S, defined as follows:
(12) The closer cP is to C,, and the less the difference between S, and S,, the closer the predicted concentra-
distribution is greater. At larger wind shear angles, existing fumigation models do not predict that such large area will be seriously polluted. (d) Comparison of ground concentration. Figure 5 compares the predicted SF, concentrations using WSFM for c( = 0” and for observed 01with the observed concentrations for the two day conditions when a TIBL and a wind direction shear existed. The dashed lines correspond to a factor of two greater and less than the observed value. The percentage of predicted values falling within the region is about 80% for the case where c(equals observed values but about 55% if wind shear direction is not included for the calculation (GI= 00). The figures indicate better agreement at high concentrations. Figure 6 shows a comparison of predicted and observed concentrations for a very large coal fired generating station at Nanticoke Complex in Ontario, Canada. Data are from Misra and Onlock (1982) and Hoff et al. (1982). More than 90% of the observed values are within a factor of two of the values predicted using the mode1 proposed here.
(a)
IO0
MSFM
IO’
Observed (pg mS3)
10
10
1000
100
10,000
Observed (pg me3)
Fig. 6. The comparison between the values predicted by WFSM and the observed at Nanticoke Complex.
(b) WSFM
IO0
IO'
Observed (pg mm3)
Fig. 5. (a) Comparison between the values predicted by MFSM and the observed. (b) Comparison between the values predicted by WFSM and the observed.
Shoreline fumigation model
3379
Table 3. WSFM evaluating results for a = 0’ and for observed a
Model
C,
MSFM a = 0” WSFM Observed
C,
S,,
2.49 4.75
4.02 5.96
6.33
d
S,
- 3.84 63.07 - 1.75 31.24
(13)
,$(C,i - Co)’
(14)
(Cri - Cr)’.
(15)
I-1
Si = f ,i 1-l
The difference assessment includes estimation of the bias d; the difference between prediction and observation; the variance of the difference S’; the mean absolute gross error IdI and the mean square error MSE with its systematic component MSEs and its unsystematic component MSE,. They are defined respectively as follows:
d= jj ,i
Idl
MSE
MSE,
MSE.
h
5.58 3.47
76.38 33.61
65.96 23.42
10.43 10.19
0.59 0.85
9.55
tion to the observed one;
St = f
S2
(Cpi
-
where Cbi = Cri - C,,, Cbi = C,i - C,,. The agreement index h falls between 0 and 1. As the index approaches 1, performance of the model improves. Table 3 shows the results of evaluating the proposed model for CI= 0” and for observed CIusing these parameters. The agreement between C, and Cr, and between S, and S, is better for observed c( in the model. All of the difference evaluation parameters for observed tl are smaller than for a = 0”. Willmott’s agreement index h is 0.59 for t( = 0” and increases to 0.85 for observed a. Clearly the concentration distribution predicted by the WSFM when the direction shear is included is in better agreement with the observed values.
5. CONCLUSIONS
Coil
I-l
S* =’
jj
[(Cpi
,i
C&) - J]*
-
(17)
I-1
IdI =
Y$ ,i ICpi-
Coil
(18)
t-l
MSE = f ,i
(Cri - C,J*
(19)
1-l
MSE, = $ ,i
(c^p- C,i)*
t-l
MSE, =. ;
,;
(Cpi - c^,)’
(21)
1-l
where (3, = arCo + br and a1 and bl are the slope and the intercept of the regression line. The smaller the value of these variables, the more accurate will be the model. The larger systematic component of mean square error (MSE,) shows that the model has not yet been able to describe physical phenomena in all respects and should be further refined. The index of agreement h, is expressed as the following:
h=l-
E
;=1
fcoi - Cpi)*
iC, (Icbil + Icbil)*
(22)
The ground concentration distribution predicted by the shoreline fumigation model with wind shear (WSFM) has the following characteristics: (1) The centre line of the ground concentration deflects from the mean wind direction above the TIBL Dr to that within the TIBL D2 with increasing distance. (2) The maximum ground concentration decreases slowly with increased wind direction shear angle. (3) The width of the ground concentration horizontal distribution is greater. Increasing the area predicted to be affected by a fumigation due to an elevated plume intersecting a TIBL in a coastal region. Predicted concentration distributions are compared with observations from an SF6 tracer experiment when wind shear occurred in a coastal region. The wind shear fumigation model developed in this paper provides predictions in better agreement with observations when wind direction shear is included.
REFERENCES
Deardorff J. C. and Willis G. E. (1982) Ground-level concentrations due to fumigation into an entraining mixed layer. Atmospheric Environment 16, 1159-1170. HoflR. M., Trivett N. B. A., Millan M. M., Fellin P., Anlauf K. G., Wiebe H. A. and Bell R. (1982) The Nanticoke shoreline diffusion experiment, June 1978-111. Groundbased air quality measurements. Atmospheric Enoironment 16.439-454.
3380
LI ZHIBIAN and YAO ZENGQUAN
Lyons W. A. and Cole H. S. (1973) Fumigation and plume trapping on the shores of lake Michigan during stable onshore flows. J. appl. Met. 12, 4955’10. Misra P. K. (1980) Dispersion from tall stacks into a shoreline environment. Atmospheric Environment 14, 397-400. Misra P. K. and Onlock S. (1982) Modelling continuous fumigation of Nanticoke Generating Station plume. Atmospheric Environment 16, 479-489.
Pas&ill F. A. and Smith F. B. (1983) Atmospheric Difision, 3rd Edn. Wiley, New York, p. 437. Stunder M. and SethuRaman S. (1986) Downwind non-
uniform
mixing
in shoreline
fumigation
processes.
Boundary-Layer Met. 34, 177-184.
Van Dop H., Steenkist R. and Nieuwstadt F. T. M. (1979) Revised estimates for continuous shoreline fumigation. J. appl. Met. 18, 133-137. Willmott C. J. (1982) Some comments on the evaluation of model performance. Bull. Am. met. Sot. 63, 1309-1313. Yao Z. Q. and Li Z. B. (1992) The characteristics of turbulence and dispersion in surface layer of coastal region. J. Hydrodyn. Ser. B 3, 67-78.